Jeff,
Do you use a custom theme from Themeroller, or do you use the default framework theme? If it's the default you will need to replace these files:
- JQuery mobile css file - New file is jquery.mobile-1.3.1.min.css
- JQuery Mobile js file - New file is jquery.mobile-1.3.1.min.js
- JQuery Core js file - New name is jquery-1.9.1.min.js
If you are using a custom theme you will need to replace files 2 & 3 as stated above and instead of file 1 replace the jquery mobile structure css file with the new one - jquery.mobile.structure-1.3.1.css
A short explaination for you...
The JQuery Mobile CSS file is for all the CSS related to the JQM widgets and themes. The JQuery Mobile js file are functions specifically related to JQM. The JQuery Core file is the JQuery Mobile framework which JQM is built upon.
Also if you replace these you need to read through the JQuery change logs as well as the JQuery Mobile change logs. Make sure nothing has changed about anything you are using. Chances are you will be fine, but you may need to check.
Hope this helps.